Low-dimensional quantum spin systems display intriguing ground state properties, whi? may have important consequences for the existence of fractionalized excitations or the emergence of high-temperature superconductivity. In this thesis we consider the material in two dimensions whi? they can be good candidates of existence spin liq- uid phases. Among various materials that show promising low-temperature behaviors, the family of organic ?arge transfer salts ? -(ET)2X (with the anisotropic triangular la?ice), InCu2 / 3V1 / 3O3, Bi3 Mn4O12 (NO3 )(BMNO) and Cu3 Ni2SbO6 (with the honey- comb la?ice) represent a very important candidate for hosting spin-liquid properties. So we study these compounds with two di?erent te?niques: 1- ?antum variational Monte Carlo for transfer salts and 2- Modi?ed spin wave for other compounds that they are mentioned above. 1- By using variational wave functions and quantum Monte Carlo te?niques, we inves- tigate the complete phase diagram of the Heisenberg model on the anisotropic triangu- lar la?ice, where two out of three bonds have superex?ange couplings J and the third one has instead J ? . ?is model interpolates between the square la?ice and the isotropic triangular one, for J ?/J ? 1, and between the isotropic triangular la?ice and a set of decoupled ?ains, for J/J ? ? 1. We consider all the fully symmetric spin liquids that can be constructed with the fermionic projective-symmetry group 1 / 2 model, with the same couplings for all the equivalent neighbors, we ?nd three phase in terms of frustration parameter ? ¯ = J 2 /J 1 : (1) a commensurate collinear ordering with staggered magnetization (Neel.I state) for 0 . 0 ? ? ¯ ? 0 . 207, (2) a mag- netically gapped disordered state for 0 . 207 ? ¯ 0 . 396, preserving all the symmetries of the Hamiltonian and la?ice, hence by de?nition is a quantum spin liquid (QSL) state and (3) a commensurate collinear ordering in whi? two out of three nearest neighbor magnetizations are antiparallel and the remaining pair are parallel (Neel.II state), for 0 . 396 ? ¯ 1 . 0. We also explore the phase diagram of distorted J 1 ? J 2 model with S = 1 / 2. Distortion is introduced as an inequality of one nearest neighbor coupling with the other two. ?is yields a ri?er phase diagram by the appearance of a new gapped QSL, a gapless QSL and also a valence bond crystal (VBC) phase in addition to the previously three phases found for undistorted model.